In [1]}, Mondello and Panov gave an angle constraints of the existence of CSC-1 irreducible metrics with finite singularities on \(S^{2}\) . In [2]}, Eremenko gave the angle constraints of reducible metrics. Our purpose in this paper is to study the structure of CSC-1 reducible conformal metrics on any compact Rieamnn surface. Moreover, we want to give the angle constraints of the existence of CSC-1 conformal reducible metrics with finite conical singularities on a compact Rieamnn surface with genus \(g\ge 1\) . Our motivation comes from the papers [3]},[4]},[5]},[6]} and [1]}.
